A357150 Primitive terms in A357148.

1, 3, 5, 7, 9, 15, 16, 24, 29, 32, 33, 34, 36, 42, 61, 64, 65, 72, 76, 82, 85, 91, 100, 104, 116, 127, 128, 129, 133, 144, 146, 153, 154, 169, 172, 179, 192, 209, 224, 256, 257, 258, 260, 262, 264, 270, 276, 281, 303, 322, 325, 339, 355, 356, 360, 400, 417, 418

Offset

1,2

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Bitmap of a(n), n = 1..2^10, 6X vertical exaggeration, read horizontally where black represents 1 and white 0, with least significant bit on bottom.

Scott R. Shannon, Image for n=1..28000.

Example

Let b(n) = A357082(n).
3 is in the sequence since S = b(1) + b(2) = 1 + 2 = 3. Since b(3) = 3, it is not possible to see S = 3 again.
4 is not in the sequence since no sum S = 4 appears before b(4) = 4 = "100" in binary, whereafter "100" is appended to W, and thereafter prohibited as a sum of adjacent terms in b for n > 4.
32 is in the sequence since S = b(11) + b(12) = b(16) + b(17) = b(23) + b(24) = 32. We note that b(31) = 32, therefore these are the only instances of sum S = 32.

Mathematica

nn = 650; s[_] = c[_] = False; j = 0; i = u = 1; w = "0"; b = Reap[Do[k = u; While[Or[c[k], StringContainsQ[w, Set[v, IntegerString[j + k, 2]]]], k++]; c[k] = True; Sow[k]; If[! s[#], Set[{a[i], s[#]}, {#, True}]; i++] &[j + k]; Set[{j, w}, {k, w <> IntegerString[k, 2]}]; If[k == u, While[c[u], u++]], {n, nn}] ][[-1, -1]]; TakeWhile[Array[a, i - 1], MemberQ[b, #] &]

Crossrefs

Cf. A357082, A357148.

Sequence in context: A357148 A268496 A121820 * A351462 A258159 A238257

Adjacent sequences: A357147 A357148 A357149 * A357151 A357152 A357153

Keyword

nonn

Author

Michael De Vlieger, Sep 15 2022

Status

approved